Yes basically dividing the base gives the closest power possible , your right thank you.

Actually still need help.om this problem, what does it mean Lg or ln? I understand the decimal digit number like 7.144 is the exact amount of power to get 20000 using base 4, .144 is the rest of the remainder but how do you that decimal number without multiplying 4 times itself many times the results? And how would you use that number to get 20000 with the base 4 exactly?